Question

How do you solve $4x+6=2x+4$?

Answer 1

Hint: In this question, we need to solve the given equation to find the value of x which satisfies the equation. For this we need an equation of the form x = c where c is constant i.e. we need variable x on one side and constant term on the other side. We will use certain operations i.e. addition, subtraction, multiplication, division to convert the equation in the form x = c. The value of constant will give us the required value of x which satisfies the equation.

Complete step by step answer:
Here we are given the equation in terms of x as $4x+6=2x+4$.
We need to find the value of x which satisfies this equation. For this let us use certain operations such as addition, subtraction, multiplication, division so that variable x is on the left side of the equation and constant term is left at the right side of the equation. The equation is given as $4x+6=2x+4$.
As we can see, the left side of the equation contains a constant term which is not needed. So let us remove it. For removing it let us subtract 6 from both sides of the equation we get $4x+6-6=2x+4-6$.
Simplifying the left side we get $4x=2x+4-6$.
Solving 4-6 we know that 6-4 = 2 but negative sign is with 6 which is greater so we have 4-6 = -2.
Therefore the equation becomes $4x=2x-2$.
Now the right side of the equation has a variable term which is not required. So let us remove it by subtracting both sides by 2x we get $4x-2x=2x-2-2x\Rightarrow 4x-2x=-2$.
In the left side of the equation both terms are like terms with variable x so solving it to get a single term we get $4x-2x$ as 2x we have $2x=-2$.
The equation is not in the form x = c as x has a coefficient. So let us remove this coefficient. For this, let us divide both sides by 2 we get $\dfrac{2x}{2}=\dfrac{-2}{2}$.
We know 2 divided by 2 gives 1 so our equation becomes x = -1.
Hence the required value of x is -1 which will satisfy the given equation.

Note:
Students should take care of the signs while solving the equation. Use proper operations as required. Students can check their answer in following way,
Putting x = -1 in the original equation $4x+6=2x+4$ we get $4\left( -1 \right)+6=2\left( -1 \right)+4$.
Simplifying we get $-4+6=-2+4\Rightarrow 2=2$.
Left hand side is equal to the right hand side of the equation. Therefore, x = -1 is the correct answer.